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Beyond X's and Y's: M aking A lgebraic T hinking H appen. Columbus Regional Mathematics Collaborative October 2013. Welcome. http:// www.youtube.com/watch?v=yQej8AOjEHc.

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beyond x s and y s m aking a lgebraic t hinking h appen

Beyond X's and Y's: MakingAlgebraic Thinking Happen

Columbus Regional Mathematics Collaborative

October 2013

welcome
Welcome
  • http://www.youtube.com/watch?v=yQej8AOjEHc
slide3

Can your students solve for a variable? Balance equations? Solve a proportion? That's only part of the story! Students who can "do" algebra do not, necessarily, think algebraically. Yet, algebraic reasoning forms the core of the middle grades CCGPS standards. Learn ways to improve students’ algebraic thinking without relying on a procedural approach, while engaging them in meaningful problem solving and discourse. Help students discover that mathematics involves creativity and non-routine thinking.

speed dating approach to algebraic thinking
“Speed Dating” Approach to Algebraic Thinking
  • Introduce a variety of topics
  • Whet your mathematical appetite
  • Contact us for help/clarification
  • Resources will be located at http://crmc.columbusstate.edu/
modeling solving equations with algebra tiles
Modeling & Solving Equations with Algebra Tiles

http://illuminations.nctm.org/ActivityDetail.aspx?ID=216

x + 5 = -8

3x = -12

- x – 3 = 8

3x – 2 = 4x + 5

-2x + 7 = 3x – 3

3x – 5 – 4x = 6 – 2x + 1

equations with fractional coefficients
Equations with Fractional Coefficients
  • Making fractional coefficients have meaning
  • Using…
      • Pattern Blocks
      • Two-color counters

x = 20

  • x = 6
  • x = 9
proportional reasoning
Proportional Reasoning
  • Making the relationships explicit
  • Using…
      • Square tiles
      • Tables
  • Introduce a pictorial representation before introducing
slide9

We have observed that the M&M’s company seems to make 3bluecandies for every 5 non-blue candies. How many non-blue candies would you expect to find in a bag with 27 blue candies?

slide10

A family bought 12-pack Cokes to serve at their football party.  There were 18 people at the party.  They used 4 ½ packs of the 12-pack drinks.

Next year the party will be expanded, and there will be 24 people.  How many 12-pack Cokes should the family buy?

percent problems
Percent Problems
  • A tool to make symbolic relationships visual
  • Using…
    • Dot paper

1. The PTA reported that 75% of the total number of families were represented at the meeting. If students from 320 families go to the school, how many were represented at the meeting?

2. Zane bought his new computer at a 37½% discount. He paid $700. How many dollars did he save by buying it at a discount?

3. The hardware store bought widgets at 80 cents each and sold them for $1 each. What percent did the store mark up the price of each widget?

systems of equations
Systems of Equations
  • Using algebra tiles to model the mathematics
  • Making relationships explicit
  • Solving by
      • Substitution
      • Elimination
solving by elimination
Solving by Elimination

x + y = 5

x – y = 5

2x + y = 5

2x + 3y = 11

2x + y = 7

x – 2y = 6

solving by substitution
Solving by Substitution

y = 2x + 3

3x + 2y = 20

x = -y + 5

2x + 4y = -6

x = y + 3

-2x – 3y = 4

gizmos exciting new
Gizmos: Exciting & New
  • http://www.explorelearning.com/
  • The world's largest library of interactive online simulations for math and science education in grades 3-12
  • Simulations called Gizmos
  • Subscription required
farewell on a light note
Farewell on a Light Note
  • First, pick the number of times a week that you would like to have chocolate (more than once but less than 10….. 1)
  • Multiply this number by 2
  • Add 5
  • Multiply by 50
  • If you have already had your birthday this year, add 1763. If you haven't, add 1762.
  • Now subtract the four-digit year that you were born.
  • You should have a three-digit number.
  • The first digit of this is your original number (how many times you want to have chocolate each week).
  • The next two numbers are…YOUR AGE!

How does this work?